Why Hugo the dachshund sleeps in the aquarium – weird theories with propositional logic

Illustration Susanne Gold, Text Aenne Barnard

A little over a year ago – just before Corona – I attended my first yoga class, with lots of “Ooohhmm”, singing bowls, scented oil and chanting. Lilly(name changed) explained not only how to do the perfect sun salutation, but also all sorts of esoteric-alternative-medicinal stuff, like which scent stimulates which powers and which yoga posture helps ward off illness. Their advice was not my world, even then. My body only gets therapies that have been scientifically proven to be effective. But Lilly’s view of things didn’t bother me either; it wouldn’t have occurred to me to initiate a discussion about medical studies. Why should it? It’s her business what she believes. Besides, I have rarely seen a person who seemed as content as Lilly on the yoga mat.

The rage of one and the others

It was easy to be tolerant back then and then the pandemic came. Now I’m angry when people ignore science. I could only scream when I see people denying the facts at demonstrations and claiming, for example, that there is no pandemic at all. “Are you idiots!”, I want to shout. “You’re only making things worse. Can’t you see that the scientists have always been right with their words of warning for a year now?”

Obviously they can’t hear, they don’t even want to, because they are angry too. They call the press liars, they fear a corrupt system that steals their freedom and they claim all kinds of strange things.

Tolerance for each other’s opinions has become almost impossible for both sides, because each other’s opinions become an existential threat. How could it have come to this?

Tertium non datur – Truth and lies in logic

There are certainly many possible explanations, one of which is propositional logic – a mathematical formalism for describing the relationships between propositions. Statements, these are assertions that are either true or false (tertium non datur, there is no third possibility). Examples of statements are: “ice is cold”, “three is greater than five”, “monkeys are not camels”.

If we have a few true basic assumptions (logicians speak of axioms), then we can derive further true statements with the help of propositional logic. For example, if we know the axioms “Hugo is a dachshund” and “Every dachshund is a dog”, then we can deduce that “Hugo is a dog” is also true.

But woe betide us if a single false one has crept in among our axioms, such as “Hugo the dachshund is a goldfish”. In this case, we can derive interesting statements without any further error in thinking. For example: “Some dogs have gills”, or “Dachshund Hugo sleeps in the aquarium”.

“Es falso quotlibet”, the logicians say to this. “Anything can be inferred from the false”. A false basic axiom is enough, and there are no limits to the creativity of assertions.

A decisive axiom – What is good medicine?

We are allowed (in this time, in this country) to avail ourselves of extensive medical treatments that have been proven effective in many studies – what a privilege. At the same time, some people – and not a few with high education – believe that there are better alternatives, that crystals, scented oils or extremely diluted substances have more effect than tested medicines. They often reject prevention through vaccination completely. The mindset of these people could therefore be shaped by the following axioms: Axiom 1 “classical medicine is bad” and Axiom 2 “vaccinating is dangerous”.

So now during the pandemic, a hypothetical train of thought (by logical reasoning alone) might be as follows.

1. I conclude that our political decision makers are relying solely on bad classical medicine, which is very bad (because of Axiom 1).
2. Consequently, they are very stupid because they do not realise what is good, or they have other goals because they do not care for people well.
3. The political decision-makers support the vaccination campaigns. This is super dangerous (because of Axiom 2). So the decisions of the politicians endanger the people.
4. Whoever has come this far intellectually now only needs a little bit of imagination and the conspiracy theory is perfect.

And now? And how do we get out of this logic dilemma? What could the vision for the future look like? I don’t know, probably a long rocky road of – don’t restrict freedom of expression – facts, facts, contradiction and more facts.

By the way, my yoga class last spring was cancelled halfway through, due to lockdowns. I haven’t seen Lilly since. I hope she is doing well.


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